Answer:
-12.85 °C is the lowest possible melting point for engine coolant that is 30% ethylene glycol.
Explanation:
[tex]\Delta T_f=iK_f\times m[/tex]
[tex]Delta T_b=i\times K_b\times \frac{\text{Mass of ethylene glycol}}{\text{Molar mass of ethylene glycol}\times \text{Mass of water in Kg}}[/tex]
where,
[tex]\Delta T_f[/tex] =depression in boiling point
i = van't Hoff factor = 1 (organic compounds)
Mass of ethylene glycol = 30 % of 100 g solution :
= [tex]\frac{30}{100}\times 100 g=30 g[/tex]
Mass of water=100 g - 30 g = 70 g = 0.070 kg (1 kg = 1000 g)
[tex]K_b[/tex] = freezing point constant = 1.86 °C/m
m = molality
Now put all the given values in this formula, we get:
[tex]\Delta T_f=1\times 1.86 ^oC/m\times \frac{30 g}{62 g/mol\times 0.070 kg}[/tex]
[tex]\Delta T_f=12.85^oC[/tex]
Freezing pint of pure water = T = 0°C
Freezing point of 30 % ethylene glycol solution = [tex]T_f[/tex]
[tex]\Delta T_f=T-T_f[/tex]
[tex]T_f=0^oC-12.85^oC=-12.85^oC[/tex]
-12.85 °C is the lowest possible melting point for engine coolant that is 30% ethylene glycol.
